Finite Group Databasebeta

← Group #11776043

Character table — Group #11776043

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222444444444444444666666888888888888812121212121212121216161616161624242424242424242424242424242424242472727272
order1222334444666666346661212121212121212121244121212122466121212121212121212244661212121266612121224668888121224242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111111-1-1-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1
χ9111111-1-1-1-111111111111-1-1-1-111-1-1-1-11111111-1111-1-1-1-1-1-1111-1-111-1-1-1-1111-1-1-1-11-1-1i−ii−i11ii−i−iii−i−ii−ii−i
χ10111111-1-1-1-111111111111-1-1-1-111-1-1-1-11111111-1111-1-1-1-1-1-1111-1-111-1-1-1-1111-1-1-1-11-1-1−ii−ii11−i−iii−i−iii−ii−ii
χ11111111-1-1-1-111111111111-1-1-1-111-1-1-1-1111111-11-1-1111-1-1-1-1111-1-111-1-1-1-1-1-1-11111-111i−i−ii-1-1ii−i−i−i−iiii−i−ii
χ12111111-1-1-1-111111111111-1-1-1-111-1-1-1-1111111-11-1-1111-1-1-1-1111-1-111-1-1-1-1-1-1-11111-111−iii−i-1-1−i−iiiii−i−i−iii−i
χ13111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-111-111-1-11111111-1-1-11-111i−ii−i-1-1ii−i−iii−i−i−ii−ii
χ14111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-111-111-1-11111111-1-1-11-111−ii−ii-1-1−i−iii−i−iiii−ii−i
χ15111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-111-1-11111-1-1-1111-11-1-1i−i−ii11ii−i−i−i−iii−iii−i
χ16111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-111-1-11111-1-1-1111-11-1-1−iii−i11−i−iiiii−i−ii−i−ii
χ1722222222-2-22222222-222222-2-2-2-222-2-22222220000-20022-2-2-2-2-22-2-2-222-2-20000000000000000000000000000
χ1822222222-2-22222222-222222-2-2-2-222-2-2-2-2-2-2-2-20000-20022-2-2-2-22-2222-2-2220000000000000000000000000000
χ19222222-2-2222222222-2222-2-222-2-2-2-2222222220000-200-2-222-2-2-2-22-2-2-2-2220000000000000000000000000000
χ20222222-2-2222222222-2222-2-222-2-2-2-222-2-2-2-2-2-20000-200-2-222-2-222-22222-2-20000000000000000000000000000
χ2122222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-1222222-1-1-1-122-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-12-1-12-1-122-1-10000-1-1000000000000
χ2222222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-1222222-1-1-1-1-2-211211-1-1-1-1-1-1222-1-1-1-1-1-1-211-211-2-211000011000000000000
χ2322222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-12222-2-2111122-1-12-1-1-1-1-1-1-1-1-2-2-21111112-1-12-1-1-2-211000011000000000000
χ2422222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-12222-2-21111-2-211211-1-1-1-1-1-1-2-2-2111111-211-21122-1-10000-1-1000000000000
χ2522222-122-2-2222-1-1-1-1-2-1-1-1-1-1111122-2-222-1-1-1-100−i3i3-2−i3i3-1-11111-22-211-1-1110−i3i30−i3i300−i3i30000−i3i3000000000000
χ2622222-122-2-2222-1-1-1-1-2-1-1-1-1-1111122-2-222-1-1-1-100i3−i3-2i3−i3-1-11111-22-211-1-1110i3−i30i3−i300i3−i30000i3−i3000000000000
χ2722222-122-2-2222-1-1-1-1-2-1-1-1-1-1111122-2-2-2-2111100−i3i3-2−i3i3-1-111112-22-1-111-1-10−i3i30−i3i300i3−i30000i3−i3000000000000
χ2822222-122-2-2222-1-1-1-1-2-1-1-1-1-1111122-2-2-2-2111100i3−i3-2i3−i3-1-111112-22-1-111-1-10i3−i30i3−i300−i3i30000−i3i3000000000000
χ2922222-1-2-222222-1-1-1-1-2-1-1-111-1-111-2-22222-1-1-1-100−i3i3-2i3−i311-1-111-2-221111-1-10−i3i30i3−i300i3−i30000−i3i3000000000000
χ3022222-1-2-222222-1-1-1-1-2-1-1-111-1-111-2-22222-1-1-1-100i3−i3-2−i3i311-1-111-2-221111-1-10i3−i30−i3i300−i3i30000i3−i3000000000000
χ3122222-1-2-222222-1-1-1-1-2-1-1-111-1-111-2-222-2-2111100−i3i3-2i3−i311-1-11122-2-1-1-1-1110−i3i30i3−i300−i3i30000i3−i3000000000000
χ3222222-1-2-222222-1-1-1-1-2-1-1-111-1-111-2-222-2-2111100i3−i3-2−i3i311-1-11122-2-1-1-1-1110i3−i30−i3i300i3−i30000−i3i3000000000000
χ3322222-1-2-2-2-2222-1-1-1-12-1-1-11111-1-1-2-2-2-222-1-1-1-12-2-1-12111111-1-12-2-2-1-111112-1-1-211-22110000-1-1000000000000
χ3422222-1-2-2-2-2222-1-1-1-12-1-1-11111-1-1-2-2-2-222-1-1-1-1-22112-1-11111-1-12-2-2-1-11111-2112-1-12-2-1-1000011000000000000
χ3522222-1-2-2-2-2222-1-1-1-12-1-1-11111-1-1-2-2-2-2-2-211112-2-1-12111111-1-1-22211-1-1-1-12-1-1-2112-2-1-1000011000000000000
χ3622222-1-2-2-2-2222-1-1-1-12-1-1-11111-1-1-2-2-2-2-2-21111-22112-1-11111-1-1-22211-1-1-1-1-2112-1-1-22110000-1-1000000000000
χ372222-122222-1-1-1222-12-1-1-1222222-1-1-1-10000002222-122-1-1-1-1-1-1000000000-1-1-1-1-1-10000222200-1-1-1-1-1-1-1-10000
χ382222-122222-1-1-1222-12-1-1-1222222-1-1-1-10000002222-122-1-1-1-1-1-1000000000-1-1-1-1-1-10000-2-2-2-200111111110000
χ392222-122222-1-1-1222-12-1-1-1222222-1-1-1-1000000-2-2-2-2-1-2-2-1-1-1-1-1-1000000000111111000022-2-200-1-1-1-111110000
χ402222-122222-1-1-1222-12-1-1-1222222-1-1-1-1000000-2-2-2-2-1-2-2-1-1-1-1-1-10000000001111110000-2-222001111-1-1-1-10000
χ412222-12-2-2-2-2-1-1-1222-12-1-1-1-2-2-2-22211110000002-222-1-2-21111-1-1000000000-1-1-111100002i−2i2i−2i00−i−iii−i−iii0000
χ422222-12-2-2-2-2-1-1-1222-12-1-1-1-2-2-2-22211110000002-222-1-2-21111-1-1000000000-1-1-11110000−2i2i−2i2i00ii−i−iii−i−i0000
χ432222-12-2-2-2-2-1-1-1222-12-1-1-1-2-2-2-2221111000000-22-2-2-1221111-1-1000000000111-1-1-100002i−2i−2i2i00−i−iiiii−i−i0000
χ442222-12-2-2-2-2-1-1-1222-12-1-1-1-2-2-2-2221111000000-22-2-2-1221111-1-1000000000111-1-1-10000−2i2i2i−2i00ii−i−i−i−iii0000
χ454444-2444-4-4-2-2-2444-2-4-2-2-244-4-4-4-4-2-2220000000000200-2-222220000000000000000000000000000000000000
χ464444-24-4-444-2-2-2444-2-4-2-2-2-4-444-4-422-2-2000000000020022-2-2220000000000000000000000000000000000000
χ474444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-2-200000044-2-2-2-2-2111111000000000-211-2110000000000000000000000
χ484444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-2-2000000-4-422-2221111110000000002-1-12-1-10000000000000000000000
χ494444-2-244-4-4-2-2-2-2-2-21-4111-2-22222-2-22200000000−2i32i32−2i32i311-1-1-1-10000000000i3−i30i3−i30000000000000000000000
χ504444-2-244-4-4-2-2-2-2-2-21-4111-2-22222-2-222000000002i3−2i322i3−2i311-1-1-1-10000000000−i3i30−i3i30000000000000000000000
χ514444-2-2-4-444-2-2-2-2-2-21-411122-2-22222-2-200000000−2i32i322i3−2i3-1-111-1-10000000000i3−i30−i3i30000000000000000000000
χ524444-2-2-4-444-2-2-2-2-2-21-411122-2-22222-2-2000000002i3−2i32−2i32i3-1-111-1-10000000000−i3i30i3−i30000000000000000000000
χ534444-2-2-4-4-4-4-2-2-2-2-2-2141112222-2-222220000004-4-2-2-222-1-1-1-111000000000-2112-1-10000000000000000000000
χ544444-2-2-4-4-4-4-2-2-2-2-2-2141112222-2-22222000000-4422-2-2-2-1-1-1-1110000000002-1-1-2110000000000000000000000
χ5544-4-444004i−4i4-4-44-4-4404-4-4004i−4i00004i−4i0000000000000004i−4i000000000000000000000000000000000000000
χ5644-4-44400−4i4i4-4-44-4-4404-4-400−4i4i0000−4i4i000000000000000−4i4i000000000000000000000000000000000000000
χ5744-4-44-2004i−4i4-4-4-222-20-22200−2i2i00004i−4i002323−23−23000000000−2i2i000000000−2i32i30000000000000000000000000000
χ5844-4-44-2004i−4i4-4-4-222-20-22200−2i2i00004i−4i00−23−232323000000000−2i2i0000000002i3−2i30000000000000000000000000000
χ5944-4-44-200−4i4i4-4-4-222-20-222002i−2i0000−4i4i002323−23−230000000002i−2i0000000002i3−2i30000000000000000000000000000
χ6044-4-44-200−4i4i4-4-4-222-20-222002i−2i0000−4i4i00−23−2323230000000002i−2i000000000−2i32i30000000000000000000000000000
χ6144-4-4-24004i−4i-2224-4-4-20-222004i−4i0000−2i2i000000000000000−2i2i000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000
χ6244-4-4-24004i−4i-2224-4-4-20-222004i−4i0000−2i2i000000000000000−2i2i000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000
χ6344-4-4-2400−4i4i-2224-4-4-20-22200−4i4i00002i−2i0000000000000002i−2i000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000
χ6444-4-4-2400−4i4i-2224-4-4-20-22200−4i4i00002i−2i0000000000000002i−2i000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000
χ654-44-4444i−4i00-44-4-44-440-44-44i−4i00004i−4i0000000000000004i−4i00000000000000000000000000000000000000000
χ664-44-444−4i4i00-44-4-44-440-44-4−4i4i0000−4i4i000000000000000−4i4i00000000000000000000000000000000000000000
χ674-44-44-24i−4i00-44-42-22-202-22−2i2i00004i−4i000023−2323−230000000−2i2i000000000−2i32i3000000000000000000000000000000
χ684-44-44-24i−4i00-44-42-22-202-22−2i2i00004i−4i0000−2323−23230000000−2i2i0000000002i3−2i3000000000000000000000000000000
χ694-44-44-2−4i4i00-44-42-22-202-222i−2i0000−4i4i000023−2323−2300000002i−2i0000000002i3−2i3000000000000000000000000000000
χ704-44-44-2−4i4i00-44-42-22-202-222i−2i0000−4i4i0000−2323−232300000002i−2i000000000−2i32i3000000000000000000000000000000
χ714-44-4-244i−4i002-22-44-4-202-224i−4i0000−2i2i000000000000000−2i2i000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000
χ724-44-4-244i−4i002-22-44-4-202-224i−4i0000−2i2i000000000000000−2i2i000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000
χ734-44-4-24−4i4i002-22-44-4-202-22−4i4i00002i−2i0000000000000002i−2i000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000
χ744-44-4-24−4i4i002-22-44-4-202-22−4i4i00002i−2i0000000000000002i−2i000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000
χ754-4-44440000-4-44-4-4440-4-4400000000004-44-4-4400000000000000000000000000000000000000000000000000
χ764-4-44440000-4-44-4-4440-4-440000000000-44-444-400000000000000000000000000000000000000000000000000
χ774-4-444-20000-4-4422-2-2022-20000−2i32i300004-4-222-200000000000−2i32i3000−2i32i300000000000000000000000000000000
χ784-4-444-20000-4-4422-2-2022-20000−2i32i30000-442-2-2200000000000−2i32i30002i3−2i300000000000000000000000000000000
χ794-4-444-20000-4-4422-2-2022-200002i3−2i300004-4-222-2000000000002i3−2i30002i3−2i300000000000000000000000000000000
χ804-4-444-20000-4-4422-2-2022-200002i3−2i30000-442-2-22000000000002i3−2i3000−2i32i300000000000000000000000000000000
χ8188-8-8-4-4008i−8i-444-444202-2-200−4i4i0000−4i4i0000000000000002i−2i000000000000000000000000000000000000000
χ8288-8-8-4-400−8i8i-444-444202-2-2004i−4i00004i−4i000000000000000−2i2i000000000000000000000000000000000000000
χ838-88-8-4-48i−8i004-444-4420-22-2−4i4i0000−4i4i0000000000000002i−2i00000000000000000000000000000000000000000
χ848-88-8-4-4−8i8i004-444-4420-22-24i−4i00004i−4i000000000000000−2i2i00000000000000000000000000000000000000000
χ858-8-88-48000044-4-8-88-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-4-4000044-444-420-2-220000−4i34i30000000000000000000002i3−2i30000000000000000000000000000000000000
χ878-8-88-4-4000044-444-420-2-2200004i3−4i3000000000000000000000−2i32i30000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.